Question

A wire PQRS carrying a current $I$ runs along three edges of a cube of side $l$ as shown. There exists a uniform magnetic field of magnitude $B$ along one of the sides of the cube. The magnitude of the force acting on the wire is

• A. $\text{Zero}$
• B. $IlB$
• C. $\sqrt{2}IlB$
• D. $2IlB$

Answer 1

The correct option is C $\sqrt{2}IlB$

Let magnetic field be along PQ.
Force on PQ, $F_{PQ}=I(\overrightarrow{l}\times \overrightarrow{B)}=IlB\sin 0=0$
Force on QR, $F_{QR}=I(\overrightarrow{l}\times \overrightarrow{B})=IlB\sin 90=IlB$
Force on RS,
$F_{RS}=IlB\sin 90=IlB$
These force are $\perp$ to each other so.
Net force $F_{net}=\sqrt{(IlB{)}^2+(IlB{)}^2}=\sqrt{2}IlB$
$\therefore \left(c\right)$ is the correct option.